The principal at a school recorded the color and make of all vehicles in the student parking lot. From the data, the following probability model was created about the colors of the vehicles.
A 2-column table with 4 rows. Column 1 is labeled outcome with entries red, black, white, other. Column 2 is labeled probability with entries 0.28, 0.30, 0.22, 0.20.
Which pairs of events about a vehicle are mutually exclusive? Check all that apply.
The events red and black
The events white and two door
The events white and other
The events black and truck
The events red and other

The probability is defined as the chances of happening any event. Mutually exclusive events are those in which the one event is independent of the other event.

The condition for the mutually exclusive event will be:

[tex]P(A|B)=\dfrac{P(A) \ and P(B)}{P(A)}=P(A)[/tex]

We have the data

red, 0.28

black, 0.30

white, 0.22

other 0.20

Here we will check the mutually exclusive event:-

(1)The events red and black

[tex]P(R|B)=\dfrac{P(R\ and\ B)}{P(B)}[/tex]

[tex]P(R|B)=\dfrac{0.28\times 0.30}{0.30}=0.28 =P(R)[/tex]

Hence the event is exclusive.

(2)The events white and other

[tex]P(W|O)=\dfrac{P(W\ and\ O)}{P(O)}=P(W)[/tex]

[tex]P(W|O)=\dfrac{ 0.22\times 0.20}{0.20}=0.22=P(W)[/tex]

Hence the event is exclusive.

(3) The events red and other

[tex]P(R|O)=\dfrac{P(R\ and\ O)}{P(O)}=P(R)[/tex]

[tex]P(R|O)=\dfrac{ 0.28\times 0.20}{0.20}=0.28=P(R)[/tex]

Hence the event is exclusive.

Hence the events ,The events red and black ,The events white and other, The events red and other are mutually exclusive.

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